NEXT: A Neural Network Framework for Next POI Recommendation

arXiv:1704.04576v1 [cs.IR] 15 Apr 2017

NEXT: A Neural Network Framework for Next POI Recommendation Zhiqian Zhanga , Chenliang Lia , Zhiyong Wua , Aixin Sunb , Dengpan Yea , Xiangyang Luoc a State Key Lab of Software Engineering, Wuhan University, China 430079 E-mail: {cllee,zhangzq2011,zywu}@whu.edu.cn, [email protected] b School of Computer Engineering, Nanyang Technological University, Singapore 639798 E-mail: [email protected] c State Key Lab of Mathematical Engineering and Advanced Computing, China 450001 E-mail: [email protected] Abstract The task of next POI recommendation has been studied extensively in recent years. However, developing an unified recommendation framework to incorporate multiple factors associated with both POIs and users remains challenging, because of the heterogeneity nature of these information. Further, effective mechanisms to handle cold-start and endow the system with interpretability are also difficult topics. Inspired by the recent success of neural networks in many areas, in this paper, we present a simple but effective neural network framework for next POI recommendation, named NEXT. NEXT is an unified framework to learn the hidden intent regarding user’s next move, by incorporating different factors in an unified manner. Specifically, in NEXT, we incorporate meta-data information and two kinds of temporal contexts (i.e., time interval and visit time). To leverage sequential relations and geographical influence, we propose to adopt DeepWalk, a network representation learning technique, to encode such knowledge. We evaluate the effectiveness of NEXT against state-of-the-art alternatives and neural networks based solutions. Experimental results over three publicly available datasets demonstrate that NEXT significantly outperforms baselines in real-time next POI recommendation. Further experiments demonstrate the superiority of NEXT in handling cold-start. More importantly, we show that NEXT provides meaningful explanation of the dimensions in hidden intent space.

1

Introduction

The huge volume of check-in data from various location-based social networks (LBSNs) enables studies on human mobility behavior in a large scale. Next POI recommendation, the task to predict the next POI a user will visit at a specific time point given her historical check-in data, has been studied extensively in recent years. Location recommendation is different from a typical recommendation task (e.g., movies, songs, books) because there are a wide range of contextual factors to consider. These auxiliary factors include the temporal context, sequential relations, geographical influence, and auxiliary meta-data information (such as textual description, user friendship, to name a few). Existing solutions based on matrix factorization and embedding learning techniques have delivered encouraging performance. However, these approaches often incorporate different contextual factors through a fusion strategy: modeling the factors either as weighting coefficients or additional constraints (Cheng, Yang, Lyu, & King, 2013; Feng et al., 2015; Ye, Yin, & Lee, 2010; Ye, Yin, Lee, & Lee, 2011; Yuan, Cong, Ma, Sun, & Thalmann, 2013). The dense vector representation (i.e., embeddings) and neural networks (NN) based techniques provide a new way of modeling these factors in an unified manner. This offers two benefits: • In contrast to one-hot representation in high dimensional space, dense representation enables us to retain the semantic relatedness or constraints in the embeddings of POIs, users and their auxiliary meta-data. For example, users at Golden Gate Overlook are likely to visit Baker Beach in San Francisco, and vice versa. Therefore, Golden Gate Overlook and Baker Beach can be projected closer in the embedding space. By encoding all context factors mentioned above into corresponding embeddings or nonlinear manipulations, we expect to obtain better recommendation accuracy. 1

• The cold-start problem can be further alleviated, since both new users and POIs may be covered partially by some of the factors (e.g., textual description, friendship). With dense vector representations, we can approximate these freshers in a smooth manner. Although the outlook is encouraging, however, the challenge is how to utilize these context factors effectively in NN, and also achieve an explainable model based on the auxiliary meta-data. In this paper, we take a special interest on developing an unified neural network based framework to address the above challenge. We propose a simple but effective neural network framework for next POI recommendation task, named NEXT. With one layer of feed-forward neural network supercharged by ReLU (i.e., rectified linear unit), NEXT is able to incorporate temporal context, sequential relations, geographical influence and auxiliary meta-data information, in an integrated architecture. Specifically, NEXT utilizes one-layer of nonlinearity to learn high-level spatial intent for a user from both the user and her latest POI visit. In other words, NEXT does not calculate an inner product directly on the embeddings of users and POIs in a common hidden space as in the existing embedding learning approaches (Feng et al., 2015; Li, Cong, Li, Pham, & Krishnaswamy, 2015; Xie et al., 2016). Instead, NEXT utilizes the non-linear transformations to extract the user-based and POI-based spatial intents respectively. Empowered by this separation and nonlinearity extraction, we can incorporate temporal context, auxiliary meta-data information into the user-based and POI-based intent learning process in an integrated manner. This design also enables us to tackle the cold-start problem and deliver semantic interpretation for each individual intent dimension. To further leverage the sequential relations and geographical influence in the context of POI recommendation without feature engineering, we devise a strategy to pre-train POI embeddings. The resultant POI embeddings encode the sequential relations and geographical influence. Based on three real-world datasets, the proposed NEXT achieves significantly better recommendation performance than existing state-of-the-art approaches and neural networks based alternatives. In summary, the main contributions of this paper are as follows: • We present a novel neural network based solution for the task of next POI recommendation. The proposed NEXT is an unified framework such that temporal context, sequential relations, geographical influence and auxiliary meta-data information can be exploited naturally. By injecting meta-data information into the intent learning process, we endow NEXT with the ability to smoothly handle cold-start recommendation. • Given the textual meta-data, we show that NEXT enables the interpretable hidden feature learning for explaining the recommendations. This in turn potentially benefits cold-start. • We adopt the network representation learning technique to pre-train POI embeddings. This pre-training strategy enables us to retain the sequential relations and geographical influence for better model learning. This is a flexible strategy such that other constraints besides these two context factors can also be captured.

2

Related Work

Our work is related to two lines of literatures, POI recommendation and neural networks. We review the recent advances in both areas.

2.1 POI Recommendation The conventional collaborative filtering (CF) techniques have been widely studied for POI recommendation (Ye et al., 2010, 2011; Yuan et al., 2013). Ye et al. proposed a friend-based collaborative filtering (FCF) approach for POI recommendation based on common visited POIs of the friends (Ye et al., 2010). Temporal context information and geographical constraints were then proven to be effective for recommendation (Ye et al., 2011; Yuan et al., 2013; Yin et al., 2016). Recently, recommendation models based on matrix factorization and embedding learning have been intensively studied. Cheng et al. proposed a multi-center Gaussian model to capture user geographical influence and combined 2

it with matrix factorization model to recommend POIs (Cheng, Yang, King, & Lyu, 2012). In (Cheng et al., 2013), a tensor-based FPMC-LR model is proposed by considering the first-order Markov chain for POI transitions and distance constraints. Li et al. proposed a ranking based factorization method for POI recommendation which learns factorization by fitting the user’s preference over POIs, where the preference was measured in terms of POI visit frequency (Li et al., 2015). Feng et al. integrated sequential information, individual preference and geographical influence into a personalized ranking metric embedding model to improve the recommendation performance (Feng et al., 2015). Gao et al. introduced matrix factorization based POI recommendation algorithm with temporal influence based on two temporal properties: non-uniforms and consecutiveness (Gao, Tang, & Liu, 2012). He et al. proposed a tensor-based latent model which incorporates the date information, geographical distance and personal POI transition patterns into an unified framework (He, Li, Liao, Song, & Cheung, 2016). Zhao et al. developed a ranking-based pairwise tensor factorization framework, named STELLAR (Zhao, Zhao, Yang, Lyu, & King, 2016). STELLAR incorporates fine-grained temporal contexts (i.e., month, weekday/weekend and hour) and brings the significant improvement. These works tried to fit the model by maximizing the interaction between users and POIs, where the recommendation decision is made based on the last POI visit alone. Recently, Xie et al. proposed an embedding learning approach that utilizes a bipartite graph to model a pair of context factors in the context of POI recommendation, named GE model (Xie et al., 2016). Four pairs of context factors: POI-POI, POI-Region, POI-Time, POI-Word were modeled in an unified optimization framework. The experimental results showed that GE significantly outperforms other alternative algorithms for real-time next POI recommendation.

2.2 Neural Networks Neural networks techniques have experienced great success in natural language processing area such as language modeling (Mikolov, Karafi´at, Burget, Cernock´y, & Khudanpur, 2010; Mikolov, Chen, Corrada, & Dean, 2013), machine translation (K. Cho et al., 2014; Bahdanau, Cho, & Bengio, 2014), question answering (Wang, Liu, & Zhao, 2016), summarization (Allamanis, Peng, & Sutton, 2016), etc. The conventional neural networks such as artificial neural network (ANN) (Rumelhart, Hinton, & Williams, 1985) and multilayer perceptron (MLP) architectures (Rumelhart et al., 1985; Werbos, 1988; Bishop, 1995) are among the first invented networks. Although relatively simple, it has been proven that a MLP with a single hidden layer containing a sufficient number of nonlinear units can approximate any continuous function on a compact input domain to arbitrary precision (Hornik, Stinchcombe, & White, 1989). Recently, He et al. developed a deep neural network based matrix factorization approach for collaborative filtering with implicit feedback data (Xiangnan et al., 2017, To appear). Based on the embeddings of items and users, they applied multiple layers of MLP to extract the high-level hidden feature by maximizing user-item interactions. Among the various neural network structures, recurrent neural networks (RNN) have been widely used to model sequential data of arbitrary length with its recurrent calculation of hidden representation (Elman, 1990; Mikolov et al., 2010). RNN has been successfully adopted in the tasks like poem generation (Yan, 2016) and sequential click prediction (Y. Zhang et al., 2014). However, RNN suffers from the exploding or vanishing gradients problem (Hochreiter & Schmidhuber, 1997) such that the distant dependencies within the longer sequence could not be learnt appropriately. Two RNN variants: long short-term memory (LSTM) and gated recurrent unit (GRU), were proposed to tackle this problem to enable long-term dependency learning. LSTM utilizes three gates and a memory cell to control the information flow. It forgets the irrelevant signals by turning off the corresponding three gates and updating memory content. LSTM has been widely used in different tasks involving the sequence modeling (Chen, Qiu, Zhu, Liu, & Huang, 2015; Rockt¨aschel, Grefenstette, Hermann, Kocisk´y, & Blunsom, 2015). GRU is a recent variant of RNN with two gates and no memory cell (K. Cho et al., 2014). The two gates control the expose of the previous hidden output and the update of the new hidden output respectively. GRU has been proven to capture the long-term dependencies just like LSTM (Chung, G¨ulc¸ehre, Cho, & Bengio, 2014). There is very limited studies on using neural network for next POI recommendation. Liu et al. proposed a RNN-based neural network solution by modeling user’s historical POI visits in a sequential manner (Liu, Wu, Wang, & Tan, 2016), named STRNN. STRNN adopts timespecific transition matrices and distance-specific transition matrices in a recurrent manner under the framework of RNN model. The proposed NEXT here differs significantly from STRNN in several aspects. First, NEXT is one layer feed-forward neural network based model where only the latest POI visit is taken as input. On the contrary, STRNN 3

(and also other RNN variants) has to take all historical POI visits as input and process in a sequential (or recurrent) manner, which increases the complexity of the model. Second, while STRNN only incorporates temporal context and geographical influence for recommendation, NEXT can incorporate multiple context factors (i.e., temporal context, geographical influence, auxiliary meta-data) in an unified framework. Third, instead of applying distance-specific latent feature extraction in STRNN, NEXT encodes the sequential relations (transition behaviors and geographical information) within the pre-trained POI embeddings by adopting DeepWalk technique (Perozzi, Al-Rfou, & Skiena, 2014). Our experimental results show that NEXT delivers superior performance than the existing matrix factorization and embedding learning based models as well as the neural network based techniques.

3

Our Approach

In this section, we first formally define the research problem and then present the proposed neural network framework for next POI recommendation task, named NEXT. We introduce the basic neural architecture of NEXT to extract the hidden intents regarding the user’s next move. We then describe the mechanism to accommodate NEXT with the temporal context modeling. Next, a pre-training strategy based on the network representation technique (i.e., DeepWalk) is introduced to integrate the sequential relations and geographical influence. We also discuss the traits of NEXT to interpret the hidden intent features and handle the cold-start issue.

3.1 Next POI Recommendation We first define the problem of next POI recommendation. Given a user with a sequence of historical POI visits Lui = {qut1 , qut2 , ..., quti−1 } up to time ti−1 , the task is to calculate a score for each POI based on Lui and a time point ti . Higher score indicates higher probability that the user will like to visit that POI at time ti . The POI with the highest score will then be recommended. In most LBSNs, in addition to the sequence of historical POI visits, users and POIs are associated with auxiliary meta-data information. For example, a user could build connections with other users (e.g., friends) to share their activities and opinions. A POI could contain textual description or category labels. Here, we denote the auxiliary meta-data associated with user u and POI q as Au and Aq , respectively.

3.2 Neural Architecture Basic Model. Different from the existing works that directly take the shallow embeddings of the users and POIs for score calculation (i.e., an inner product), in NEXT, we introduce an additional feed-forward neural network layer to model user’s spatial intent, on top of the embedding. Let uu ∈ Rd be the embedding of user u, qℓ ∈ Rd be the embedding of a candidate POI qℓ to be recommended, and quti−1 ∈ Rd be the embedding of POI quti−1 , the last visited POI by user u at time ti−1 .1 We model the hidden intent of next visit by a nonlinear activation function, rectified linear unit: ReLU(x) = max(x, 0). q

(1)

u

h = ReLU(W2 uu + b2 )

(2)

cℓ = ReLU(W3 qℓ + b3 )

(3)

hti = ReLU(W1 quti−1 + b1 )

q

In the above modeling, the hidden intent vector hti is expected to capture semantics regarding the user’s next move at time ti based on her last POI visit. Intent vector hu captures user specific knowledge on spatial preference of a particular user. cℓ is the intent representation of candidate POI ℓ. W1 ∈ Rd×d and W2 ∈ Rd×d are transition matrices from POI embeddings and user embeddings respectively, to the hidden intent. W3 ∈ Rd×d is a weight matrix. b1 ∈ Rd , b2 ∈ Rd , and b3 ∈ Rd are all bias vectors. 1

For model simplicity, we set intent vectors, POI embeddings, user embeddings, word embeddings to be of the same dimension.

4

x + w2

uu

x = yu,t ,l

+

ReLU

b2

i

Score

ReLU

ReLU

Transition Matrix

x +

Intent Vector Embedding Vector

w1

Bias Vector

x +

q ti -1 b 1

w3

ql

b3

Figure 1: Basic model of NEXT, uu , qℓ and qti−1 are the embedding vectors of the user, candidate poi, and the last visited POI. With the hidden intent vectors hqti , hu , and cℓ , the recommendation score yu,ti ,ℓ of POI qℓ for user u at time ti is w computed as follows: q yu,ti ,ℓ = (hu + hti )T cℓ (4) In simple words, in NEXT, instead of directly using embedding vectors of users and POIs, a feed-forward network ) layer is used to transform the) embeddings to intent vectors. Recommendations are made based on the intent vectors. u The transition matrices and bias vectors make it possible to identify the most useful information from the embeddings. q By separating the intent vectors and embedding vectors, NEXT framework also makes it simple and straightforward to be extended by incorporating information w (tfrom ) different context factors. Figure 1 illustrates the basic model of NEXT. Incorporating Meta-data Information. Since the associated meta-data information could offer complementary knowledge about users and POIs respectively, it is expected to enhance the understanding of user movement by taking Au and Aq into consideration. Hence, we further enrich NEXT framework by taking these auxiliary semantics into the intent calculations. First, we calculate the embedding mq to represent auxiliary meta-data Aq as follows: mq =

1 X mm |Aq | m∈A

(5)

q

where mm is the embedding of item m in the meta-data Aq . Based on mq from Equation 5, we rewrite Equations 1 and 3 as follows:     q (6) hti = ReLU W1 αquti−1 + (1 − α)mqut + b1  i−1    (7) cℓ = ReLU W3 αqℓ + (1 − α)mqℓ + b3 where α works as a tuning parameter, controlling the importance of meta-data information. Similar to Equations 5 and 6, we rewrite Equation 2 with the auxiliary meta-data Au as follows: mu =

1 X mm |Au | m∈A

(8)

u

hu = ReLU W2 (βuu + (1 − β)mu ) + b2




(9)

where mm is the embedding of item m in the meta-data Au , β is a tuning parameter just like α in Equation 6. Note that the embeddings of users (i.e., uu ) and the embeddings of POIs (i.e., qq ) are not assumed to be within the same hidden space. In this sense, given the types of meta-data information are homogenous for Au and Aq , NEXT is flexible to associate two sets of embeddings for the meta-data information. This is reasonable because these two kinds of meta-data may convey very different semantics. For example, both users and POIs can be associated with 5

textual labels. While the users use labels to indicate their tastes and preferred locations, the labels of POIs may cover the related services instead. In this case, we may prefer using two separate embedding spaces.2

3.3 Incorporating Temporal Context Temporal context has been widely used in existing POI recommendation studies and proven to be effective. Here, we accommodate NEXT with temporal context by influencing the computation of the hidden intent. There are two kinds of temporal context available: (i) the time interval between two successive POI visits (i.e., ti − ti−1 ), and (ii) the particular time point of the POI visit (i.e., ti ). For example, a POI visit happened 12 hours ago could contain less guidance about the user’s current spatial intent. Similarly, users could express different spatial intents at different time slots, e.g., lunch hours. We design a mechanism to incorporate both kinds of temporal context into the POI based intent calculation (Equation 6). The time interval from the last POI visit is critical to decide the user’s next move. However, it is inappropriate to discretize temporal dimension since it is a continuous metric. It is intuitive that the historical POI visits with different time intervals could contain varying spatial intents. And the interplay between the intent and time interval could be complicated and subtle. Here we replace W1 in Equation 1 with a time interval t dependent transition matrix Wπ (t) as follows: π−t t     π W0 + π Wπ , for t < π (10) Wπ (t) =     Wπ , for t > π where W0 , Wπ ∈ Rn×d are two transition matrices, π is an interval threshold. Equation 10 adopts a linear interpolation between W0 and Wπ to derive the interval dependent transition matrix. When time interval t is close to 0, W0 is mainly in charge of intent calculation, otherwise, Wπ leads the computation when t approaches π. π works as a window, and Wπ is used only when the time interval is larger than π. As to the visit time information, we split a day into 24 time slots, each of which spans one hour (e.g., 17:00 18:00). Each time slot is associated with a specific bias vector bt . Assigning each time slot with a specific bias vector is reasonable, because users generally express different POI preferences in different time slots (Yuan et al., 2013). For example, users at the time slots of 20:00 - 22:00 prefer public entertainment. The bias vector for each time slot is expected to store such preference information and correct the mistake incurred by considering the last visited POI alone. For example, an user goes from office to a restaurant. If this transition happens in the midnoon, she probably will come back to the office again. However, it is likely for her to go home when this transition takes place at the time q period 18:00 - 20:00. With the two temporal factors, NEXT calculates the hidden intent hti as follows:     q hti = ReLU Wπ (ti − ti−1 ) αquti−1 + (1 − α)mqut + bti i−1

(11)

where bti is the bias vector of the time slot within which ti falls. Here, the interval dependent transition in Equation 10 is similar to the work in STRNN (Liu et al., 2016). However, STRNN takes all historical POIs within the interval window for consideration in a recurrent manner, which is computational expensive. Further, STRNN does not consider time-specific bias vector bti .

3.4 POI Embeddings Pre-Training The sequential relations refer to the transition probability that a user visits POI qb after visiting POI qa (i.e., qa → qb ). Hence, the transition probabilities convey the general transition patterns, (e.g., from an airport to a hotel). Also, since users like to visit the nearby POIs and their activities are often constrained into a few regions, the visiting behaviors are affected a lot by the geographical influence. Sequential relations and geographical influence are validated to be effective for the POI recommendation in many studies (E. Cho, Myers, & Leskovec, 2011; Ye et al., 2011; Li et al., 2015; J.-D. Zhang & Chow, 2015; Feng et al., 2015). 2

We leave the exploration as a part of our future work.

6

x + w2

x = yu,t ,l

+

ReLU

i

Score

b2 ReLU

ReLU

+ (1- b ) x

b x uu

x +

mu

wp (t) Transition Matrix

ax

b ti

+ (1 - a ) x q ti -1

Intent Vector Embedding Vector

x + w3

b3

+ (1 - a ) x

ax ql

mti-1

ml

Bias Vector

Meta-data Embedding Vector

POI Embeddings Pre-Training

Sequential Relations

…...

Geographical Influence

Figure 2: Overall Architecture of NEXT, mu , mℓ and mqti−1 are the embedding vectors of the meta-data associated with the user, candidate POI and the last visited POI respectively. In NEXT, we propose a POI embedding pre-training strategy to encode the sequential relations and geographical influence among POIs. Becausewthe non-convexity of the objective function in NEXT, there does not exist a global b u optimal solution. In such case, current optimization strategy is to find a local optimum. It is widely accepted that a good embedding initialization scheme could result in a faster convergence and superior performance of neural network models (Xiangnan et al., 2017, To appear). In this sense, POI embedding pre-training can also benefit the model learning. q w b w q b We adopt DeepWalk (Perozzi et al., 2014), a network representation learning technique, to learn the embedding of each POI. DeepWalk builds short sequences of nodes based on random walk over the network structure. Then a neural language model SkipGram (Mikolov et al., 2013) is adopted to learn the embeddings of the nodes by maximizing the probability of a node’s neighbor in the sequences. In order to retain these two kinds of information in the latent embedding space, we build a network structure by taking each POI as a distinct node in the network. Specifically, we create the random walk sequences over POIs by w using a mixture of both the POI transition patterns and the geographical influence. The random walk transition from POI qi to POI q j over the network is calculated as follows: q ) ) u fqi ,q j κ(qi , q j ) q + (1 − ρ) P (12) p(q j |qi ) = ρ P k κ(qi , qk ) k fqi ,qk w (t)

κ(qi , q j ) = 1/(1 + e5

d(qi ,q j )−d¯ σ(d)

)

(13)

where d(qi , q j ) denotes the Euclidean distance between POIs qi and q j by using their coordinates, d¯ and σ(d) are the mean and standard deviation of d(qi , q j ) respectively, fqi ,q j is the transition frequency from qi to q j in the training dataset. In Equation 12, the first term in the right part captures the inherent geographical influence between POIs, while the second term captures the transition behaviors of massive users. ρ is used here to balance the two components. For each POI, we generate τ random walks of length r according to Equation 12 as in (Perozzi et al., 2014). Then SkipGram language model with hierarchical softmax is applied over these random walk sequences. A POI’s embedding is learnt to maximize the probability of seeing its neighbors in the sequences. Based on Equation 12, the POIs that are close in geographical distance and likely to be visited successively by users will be closer in the embedding space. After finishing the embedding learning by SkipGram, we use the pre-trained POI embeddings as the initialization in model training. In the evaluation (Section 4), we find that this pre-training strategy delivers better recommendation performance. The overall network architecture of NEXT is illustrated in Figure 2. 7

Furthermore, we use the pre-trained POI embeddings to initialize user embedding uu . We first count the frequency of the POI a user u has visited in the training dataset, and then use the normalized frequency as the weight to calculate the initial user embedding: uu =

1 X u f · qj |Lu | j j

(14)

where |Lu | is the number of POI visits of user u in the training set, f ju is the frequency of POI q j being visited by user u.

3.5 Cold-Start and Interpretation Cold-Start. The proposed NEXT can inherently handle POI recommendation for both cold-start users and cold-start q POIs. In Equation 4, the final intent calculation is the sum of hti and huti . This additive mechanism has a potential merit for cold-start problems. Given a new user with very few historical visits (e.g., a single POI visit available), we q can directly recommend the POIs based on Equation 4 by using hti alone. Further, with Equation 9, we can calculate huti by using her meta-data information Au (i.e., by setting β = 0). This is particularly helpful for freshers that have no historical visit record. We will investigate the effectiveness of NEXT for cold-start users in Section 4.4. q For a cold-start POI q that has not been visited by any user. It is possible to calculate hti in Equation 6 based on its nearby POIs and meta-data information Aq . Interpretation. Recall that the hidden intent calculations in Equations 7, 6 and 9 use the rectified linear unit (ReLU) as the nonlinear activation function. Given ReLU generates non-negative and sparse hidden vectors, it facilitates the interpretation for each individual hidden intent dimension. For example, consider the case that word description is associated with each POI. That is, the items in Aq are the words used to describe POI q. We can get the contribution vector ω ~ w of word w by setting α = 0 in Equation 7. ω ~ w = ReLU(W3 mw + b3 )

(15)

where mw is the embedding vector of word w. Following a topical keyword re-ranking method proposed in (Song, Pan, Liu, Zhou, & Qian, 2009), we assign a score for each word under a dimension as follows: ω ~ w (i) κi (w) = P ~ w ( j) jω

(16)

where score κi (w) reflects the preference of word w under hidden dimension i. By examining the top words for each dimension in terms of κi (w), we can obtain the semantic meaning of an intent dimension. This interpretability sheds light on many new enhancements for recommendation. For example, we can allow a user to adjust the recommendation system by explicitly highlighting her preferred intent dimensions. In this way, we can add an additional bias q vector in Equation 4 to enhance this preference: yu,ti ,l = (hu + su + hti )T cl , where su is user specified intent preference. Experimental studies are presented in Section 4.5.

3.6 Training The parameters of our model are: Θ = {W∗ , M, B, U, Q, b2 , b3 }, where W∗ refers to all transition matrices W0 , W2 , W3 , Wπ ; and M contains all item embeddings for the associated meta-data of both users and POIs; B contains all time slot bias vectors bt ; U contains all user embeddings, and Q contains all POI embeddings. The model training aims to optimize above parameters such that each POI visit in the sequence of a user’s POI visits in the training set can be predicted successfully. We adopt a softmax function to calculate the predicted POI probability vector puti for user u at time ti : eyu,ti ,k (17) puti (k) = P yu,t , j je i 8

Table 1: Statistics on the three datasets. #User: the number of users; #POI: the total number of POIs; #Check-in: the total number of check-ins; #AvgC: average number of check-ins per user; #Avg(Au ): average number of items in Au ; #Avg(Aq ): average number of items in Aq . Dataset

#User

#POI

#Check-in

#AvgC

SIN Gowalla CA

1,918 5,073 2,031

2,678 7,020 3,112

155,514 252,945 105,836

81.08 49.86 52.1

Meta-data #Avg(Au) #Avg(Aq ) 4.36

2.67

Then, we use the cross-entropy error between the ground truth POI distribution (i.e., in a one-hot form) and predicted POI distribution by Equation 17 as the cost objective: Q U 1 XXX u J= qˆ (k) · log put (k) + λkΘk2 U u t∈L k t

(18)

u

where Lu is the set of historical POI visits in the training set for user u, Q is the number of all POIs under consideration, qˆ ut is the ground truth POI distribution at time t with 1-of-Q coding scheme, λ controls the importance of the regularization term, and U is the number of users under consideration. To minimize the objective, we use stochastic gradient descent (SGD) (Bottou, 1991) and back propagation to update the parameters. Although POI embeddings Q is pre-trained based on the sequential relations and geographical influence, we further fine-tune the embeddings based on the cost objective.

4

Experiments

In this section, we conduct experiments to evaluate the proposed NEXT against the state-of-the-art alternatives over three real-world datasets.

4.1 Datasets Foursquare Singapore (SIN) dataset is a collection of 194, 108 check-ins made within Singapore from 2, 321 users at 5, 596 POIs between Aug. 2010 and Jul. 2011 in Foursquare (Yuan et al., 2013). This dataset has previously been used in other studies (Yuan et al., 2013; Feng et al., 2015; Li et al., 2015). Gowalla dataset contains 736, 148 check-ins made within California and Nevada between Feb. 2009 and Oct. 2010 in Gowalla (E. Cho et al., 2011). The Gowalla dataset has previously been used in (Yuan et al., 2013; Feng et al., 2015; Li et al., 2015; Liu et al., 2016). CA dataset is a collection of 483, 813 check-ins made in Foursquare by 4, 163 users living in California. Each distinct POI is provided with a text description indicating its content. There are total 50 distinct words in all descriptions. Moreover, each user is connected to a number of other users (i.e., friendship). This dataset has previously been used in (Yin et al., 2016). Note that, this is the only dataset that contains auxiliary meta-data for both users and POIs. In all three datasets, each check-in is associated with a timestamp indicating when the user made this check-in. Following the work of PRME-G in (Feng et al., 2015), we remove the less frequent users and POIs from each dataset, such that each user has at least 10 check-ins, and each POI has been visited by at least 10 users. The data statistics on these three datasets after preprocessing is reported in Table 1. In CA dataset, there are on average 2.67 descriptive words for a POI and 4.36 friends for a user.

9

Table 2: Performance comparison over three datasets by Acc@K and MAP. The best results are highlighted in boldface on each dataset. † indicates that the difference to the best result is statistically significant at 0.05 level. Acc@1

Acc@5

SIN Acc@10

MAP

Acc@1

Gowalla Acc@5 Acc@10

PMF PRME-G Rank-GeoFM GE

0.0013†

0.0311†

0.0731†

0.0235†

0.0002†

0.0149†

0.0751†

0.1156†

0.1357†

0.0991†

0.1088†

0.0705† 0.0123†

0.1870† 0.0486†

0.2575† 0.0735†

0.1313† 0.0326†

NeuMF RNN LSTM GRU STRNN

0.025† 0.1063† 0.1032† 0.0999† 0.0826†

0.0854† 0.2397† 0.2344† 0.2211† 0.1948†

0.1341† 0.3072† 0.3015† 0.2864† 0.2636†

NEXT

0.1358

0.2897

0.3673

Method

MAP

Acc@1

CA Acc@5 Acc@10

0.0418†

0.0125†

0.0006†

0.0050†

0.0109†

0.1600†

0.1783†

0.1348†

0.0888†

0.1287†

0.1520†

0.0488† 0.0100†

0.1428† 0.0158†

0.1997† 0.0488†

0.1000† 0.0281†

0.0540† 0.0894†

0.1505† 0.1402†

0.2085† 0.1651†

0.0106† 0.1130† 0.1061† 0.1174†

0.0654† 0.1742† 0.1701† 0.1626† 0.1431†

0.0230† 0.084† 0.0868† 0.0838† 0.0557†

0.0682† 0.1859† 0.1979† 0.2015† 0.1539†

0.1082† 0.2364† 0.2535† 0.2644† 0.2081†

0.0549† 0.1376† 0.1443† 0.1454† 0.1079†

0.0437† 0.0865† 0.0931† 0.0924† 0.0713†

0.0944† 0.1877† 0.2028† 0.1974† 0.1637†

0.1361† 0.2370† 0.2583† 0.2505† 0.2181†

0.0781† 0.1397† 0.1511† 0.1482† 0.1221†

0.2127

0.1282

0.2644

0.3339

0.1975

0.1115

0.2396

0.3038

0.1772

MAP

4.2 Experimental Setup Methods and parameter settings. We compare our model against the following recent state-of-the-art POI recommendation approaches. • PMF is a method based on conventional probabilistic matrix factorization over the user-POI matrix (Salakhutdinov & Mnih, 2007). • PRME-G embeds user and POI into the same latent space to capture the user transition patterns (Feng et al., 2015). The geographical influence is incorporated in PRME-G through a simple weighing scheme. We use the recommended settings with 60 dimensions and π = 6h as in their paper. • Rank-GeoFM is a ranking based geographical factorization approach (Li et al., 2015). Rank-GeoFM learns the embeddings of users, POIs by fitting the user’s POI frequency. Both temporal context and geographical influence are incorporated in a weighting scheme. We use the recommended settings with K = 100, k = 300 as in their paper and fine-tune the parameters α and β on the development set. • Graph based Embedding (GE) jointly learns the embeddings of POIs, regions, time slots, and auxiliary metadata (i.e., descriptive words of POIs) in one common hidden space (Xie et al., 2016). The recommendation score is then calculated by a linear combination of the inner products for these contextual factors. We tune hyper-parameters N and △T on the development set. • Neural Matrix Factorization (NeuMF) is a recent state-of-the-art deep neural network based algorithm over implicit feedback (Xiangnan et al., 2017, To appear). NeuMF combines both generalized matrix factorization and MLP under one framework to learn latent features. Like PMF, we apply NeuMF over the user-POI matrix for the recommendation. The best performance is reported by tuning hyper-parameters. • STRNN is a RNN-based model for next POI recommendation (Liu et al., 2016). It incorporates both the temporal context and geographical information within recurrent architecture. • RNN is a standard RNN model for sequence modeling, upon which the above STRNN model was built (Mikolov et al., 2010). In the context of POI recommendation, the hidden feature vector huti of user u at time ti is calculated recurrently based on the whole historical POI visits: huti = σ(W4 quti−1 + Chuti−1 )

(19)

where W4 is the transition matrix from the input embedding to the hidden state, C is the state-to-state recurrent weight matrix, σ is chosen to be the sigmoid function. Following the work in (Liu et al., 2016), we calculate the recommendation score yu,ti ,ℓ of POI ℓ for user u at time ti as follows: yu,ti ,ℓ = (huti + uu )T qℓ 10

(20)

• LSTM is an variant of RNN model which contains a memory cell and three multiplicative gates to allow longterm dependency learning (Hochreiter & Schmidhuber, 1997). We calculate the recommendation score by using Equation 20. • GRU is a variant of RNN model which is equipped with two gates to control the information flow (K. Cho et al., 2014). We calculate the recommendation score by using Equation 20. Other possible alternatives are empirically found to be inferior to STRNN, PRME-G, and Rank-GeoFM, in their works respectively3 . Hence, due to space limitation, we leave these comparisons to our future work. Also, the proposed TRM model in (Yin et al., 2016) can be evaluated based on CA dataset. However, due to the shortness of POI description and smaller number of POIs after preprocessing, TRM only achieves a slightly better performance than PMF. Therefore, we exclude TRM from further comparison. The first four comparative methods listed above are conventional matrix factorization or embedding learning based techniques. The next five methods are Neural Networks based methods, which apply the nonlinearity for high-level transformation. Note that GRU and LSTM have not been evaluated in previous work on next POI recommendation task. For performance evaluation, we use the last 20% POI visits of each user as test set, the earliest 70% POI visits as training set, and the remaining 10% data as validation set to tune parameters. Metrics. Following the existing works (Xie et al., 2016; Liu et al., 2016; He et al., 2016), two standard metrics are used for performance evaluation: Acc@K and Mean Average Precision (MAP). For a specific test instance (i.e., a user visited a POI in the test set), Acc@K is 1 if the visited POI appears in the top-K ranking; otherwise 0 is taken. The overall Acc@K is the average value over all test instances. Here, we choose to report Acc@K with K = {1, 5, 10}. MAP is widely used to evaluate the quality of ranking. The higher the ground truth POI is ranked, the larger the MAP value, which indicates a better performance. Hyperparameters and Training. The interval threshold π in Equation 10 is empirically set to be 6/6/72 hours for SIN, Gowalla and CA datasets respectively. The dimensionality for the embeddings and the hidden intent are fixed to be 60 for neural network based methods for fair comparison (i.e., d = 60 in NEXT). The regularization parameter λ is 0.01 and the learning rate γ is 0.005. As to incorporating auxiliary meta-data information, we set α = 0.3, β = 0.2 in NEXT. We apply the early stop based on the validation set, or a maximum of 50 epochs are run for neural network based methods. As to POI embeddings pre-training, we set τ = 50 and r = 20 as in the original work of DeepWalk (Perozzi et al., 2014). In Equation 12, ρ = 0 is used in generating random walks for the performance comparison. The impact of ρ will be studied in Section 4.6.

4.3 Performance Comparison For performance comparison, we report the recommendation accuracy of different methods over the three datasets in Table 2, where significance test is by Wilcoxon signed-rank test. We make the following observations: First, the proposed NEXT model performs significantly better than all existing state-of-the-art alternatives evaluated here on the three datasets in all the metrics. Specifically, NEXT outperforms the conventional matrix factorization method PMF significantly by a large margin. As to the three embedding learning based solutions (i.e., PRME-G, Rank-GeoFM, GE), NEXT outperforms them by around 62.0% - 552.5%, 46.5% - 602.8% and 50.9% - 67.0% in terms of MAP metric on SIN, Gowalla and CA datasets respectively. Note that both PRME-G and Rank-GeoFM incorporate information from temporal context and geographical influence within their models on SIN and Gowalla. The large improvement suggests that high-level intent features extracted through a nonlinearity in NEXT can better catch the user’s spatial behaviors. Moreover, NEXT consistently outperforms four RNN-based methods: RNN, LSTM, GRU, and STRNN. The performance gain provided by NEXT over these four counterparts is about 22.1% - 48.6% and 35.8% - 83.0% in terms of MAP metric on the SIN and Gowalla respectively. This indicates that the mechanism to absorb two kinds of temporal context in NEXT is effective for the task of next POI recommendation. 3 Some recent works (e.g., (He et al., 2016; Zhao et al., 2016)) that incorporate POI categories and date information, are excluded for comparison, because our datasets do not contain these meta-data.

11

0.22 0.2 Acc@10

MAP

0.18 0.16 0.14 SIN Gowalla CA

0.12 0.1 0.08

0.38 0.36 0.34 0.32 0.3 0.28 0.26 0.24 0.22 0.2

SIN Gowalla CA

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Number of Dimensions

Number of Dimensions

(a) MAP

(b) Acc@10

Figure 3: Effect of the number of dimensions in NEXT Second, PMF performs the worst on three datasets in all metrics, because the user-POI matrix is very sparse on these datasets, and no temporal context or geographical influence is leveraged at all. Similar results are observed on NeuMF, a neural network based collaborative filtering technique based on implicit feedback information. Since both PRME-G and Rank-GeoFM utilize ranking based optimization strategy, the data sparsity issue is alleviated by making use of unobserved data to learn the parameters. Moreover, temporal information and geographical influence are incorporated in these two models. Therefore, a large performance improvement is obtained by PRME-G and Rank-GeoFM over PMF and NeuMF. The same phenomenon was also observed in the related works (Li et al., 2015; Feng et al., 2015; Liu et al., 2016). Third, NeuMF significantly outperforms conventional PMF. This suggests the superiority of nonlinearity for extracting hidden high-level features. As being an embedding learning technique, GE performs much worse than PRMEG and Rank-GeoFM on both SIN and Gowalla datasets. This is reasonable because no region information is available on these two datasets. The region information works as the geographical influence for GE model. However, region information is provided in CA dataset; we observe that GE achieves very close performance to PRME-G and Rank-GeoFM. Fourth, the three RNN-based methods (i.e., RNN, LSTM, GRU) perform much better than PMF, PRME-G and Rank-GeoFM in most metrics. This is consistent with our above discussion that the non-linear transformation operation as provided by the neural network models enables better high-level spatial intent learning. Although LSTM and GRU were designed to alleviate the exploding or vanishing gradients problem, no superiority is observed for them over RNN model on the SIN dataset. Reported in Table 1, the users in SIN have more POI visits on average. Because RNN-based models accumulate all historical information in the last hidden feature vector (Wang et al., 2016), the longer POI sequence could introduce much irrelevant information that hurts the performance. This result indicates that the visiting behaviors performed a long time ago are irrelevant for next POI recommendation. Also, we observe that STRNN only achieves close performance with Rank-GeoFM and PRME-G. In summary, the experimental results show that the proposed NEXT can successfully learn user’s spatial intent, leading to superior performance of next POI recommendation.

4.4 Experiments on Cold-Start Here, we evaluate the performance of NEXT and other competitors for cold-start users. Specifically, since each dataset is preprocessed to retain only active users and POIs (ref. Section 4.1), we therefore take 200 inactive users that were excluded from the training for evaluation. We conduct the experiments on CA dataset, since it is the only dataset containing auxiliary meta-data information. For each cold-start user u, we randomly pick a POI transition record (qi , q j ) such that the user visited q j after her latest visit at qi . For evaluation purpose, we restrict to the record of both qi and q j being included in the training set. Here, we test to recommend q j by utilize both her latest POI visit and meta-data. Among the baseline methods, 12

Table 3: Performance comparison for cold-start users. Method

Acc@1

Acc@5

Acc@10

MAP

PRME-G LSTM NEXT

0.0550 0.0300 0.0600

0.0650 0.1200 0.1400

0.0800 0.1900 0.1850

0.0631 0.0765 0.1045

Table 4: Top-5 words of some interpretable dimensions by NEXT. Dim 1

Dim 2

Dim 3

Dim 4

Dim 5

nightlife spot food theater movie

travel transport airport hotel store

recreation outdoors arts entertainment performing

shop service hotel office clothing

park theme venue performing drink

only PRME-G, STRNN, RNN, LSTM and GRU can be adapted here by utilizing only the POI information. STRNN, RNN, LSTM and GRU are all RNN-based models. Since LSTM achieves the best performance on CA dataset among these RNN variants (ref. Table 2), we choose LSTM as the representative, and report its performance for cold-start user recommendation. Other variants are found to be inferior than LSTM for this experiment. Table 3 reports the performance of different methods. We observe that NEXT outperforms PRME-G and LSTM in most metrics. This suggests that incorporating meta-data information is positive for addressing the recommendation for cold-start users.

4.5 Interpretation Now, we evaluate the interpretability of NEXT based on the descriptive words associated with POIs on CA dataset. We manually examine the top-10 words in terms of κi (w) for each hidden dimension i. If these top words could convey a coherent and meaningful topic reflecting a person’s activities, we consider a dimension as being interpretable. As the result, we find 34 interpretable dimensions among the 60 dimensions. Note that there are only 50 unique words used in CA dataset, and the dimension number (i.e., 60) is even larger than the number unique words. Hence, we consider this result to be excellent. To further demonstrate the superiority of NEXT in producing interpretable hidden dimensions, we list the top-5 words for 5 interpretable dimensions learnt by NEXT in Table 4. The top words in each dimension can be easily interpreted to cover a topic on a specific activity. For example, dimension 1 expresses the activity of enjoying nightlife by watching movies; dimension 3 talks about outdoors recreation such as arts performing.

4.6 Analysis of NEXT We now investigate the impact of different parameter settings in NEXT. Note that when studying a specific parameter, we set the other parameters to the values used in Section 4.2. Temporal Context. We first investigate the effect of the two kinds of temporal contexts in NEXT. Table 5 lists the performance comparison over three datasets, where Xrefers to the model with the corresponding temporal context. Observe that incorporating either time interval or visit time information leads to better performance. More performance gain is obtained by introducing the time interval dependent transition, compared to using visit time specific preference alone. This validates that the time interval since the latest POI visit plays a critical role in learning spatial intent from historical spatial behavior. Further improvement is obtained by incorporating both time interval and visit time information together. This indicates that these two kinds of temporal context provide complementary benefits for next POI recommendation. Number of Dimensions. We study the effect of the number of dimensions of hidden vectors and POI embeddings. 13

Table 5: Effect of the temporal context: time interval (TI) and time slot (TS). Dataset

TI

TS

Acc@1

Acc@5

Acc@10

MAP

X X X X X X

X X X X X X

0.1161 0.1322 0.1272 0.1358 0.0986 0.1172 0.1058 0.1282 0.0942 0.0994 0.1058 0.1115

0.2576 0.2833 0.2690 0.2897 0.2254 0.2535 0.2310 0.2644 0.2104 0.2185 0.2281 0.2396

0.3250 0.3569 0.3414 0.3673 0.2861 0.3250 0.2919 0.3339 0.2661 0.2782 0.2898 0.3038

0.1869 0.2077 0.1986 0.2127 0.1630 0.1868 0.1691 0.1975 0.1553 0.1607 0.1691 0.1772

SIN

Gowalla

CA

Table 6: Performance of NEXT on CA with varying ρ values ρ 0 0.3 0.5 0.7 1

Acc@1

CA Acc@5 Acc@10

MAP

0.0383 0.1115 0.1023 0.1015 0.1026 0.106

0.101 0.2396 0.2145 0.2077 0.2148 0.221

0.0744 0.1772 0.1626 0.1605 0.1628 0.1666

0.1406 0.3038 0.2747 0.2713 0.2779 0.2813

Here, we vary the dimension number from 10 to 100. Figure 3 shows the MAP and Acc@10 values for varying dimension numbers on the three datasets. NEXT achieves stable performance in the range of [50, 100]. We observe that NEXT outperforms RNN, LSTM and GRU even when the number of dimensions is as small as 20. The results further confirm the superiority of the proposed NEXT for next POI recommendation. POI Embeddings Pre-training. DeepWalk is used to generate POI sequences in NEXT to encode the sequential relations and geographical influence among POIs. The proportion parameter ρ is used to balance the geographical influence and transition behavior components between two POIs (Equation 12). Given the similar performance patterns observed for all three datasets, we choose to report the performance in CA dataset only, due to space limitation. Table 6 reports the performance of different ρ values over CA dataset, where symbol − refers to the model without using the pre-trained POI embeddings for initialization. First, we observe that the models initialized with pre-trained POI embeddings outperform the model without this initialization by a large margin. This validates the effectiveness of utilizing geographical distance and transition pattern between two POIs to pre-train POI embeddings. Second, all the settings with varying positive ρ values achieve similar performance. And the best performance is achieved when ρ = 0, i.e., no geographical influence factor is exploited at all. This suggests that the geographical distance and transition patterns do not contain complementary information. Based on Tobler’s first law of geography, “Everything is related to everything else, but near things are more related than distant things.” This indicates that when a user visits the next place, she will likely to visit a place near the place she visited from last time. In this sense, the geographical influence could be encoded within the transition patterns, as being validated by the results. Accordingly, we set ρ = 0 in our experiments. Auxiliary Meta-data. We further study the impact of incorporating auxiliary meta-data information to the recom-

14

0

MAP

0 0 0 al be

0 0 0

0

0

0

0

1

The

Figure 4: Performance of NEXT with different β and α values by fixing α = 0.3 and β = 0.2 respectively. Table 7: Impact of incorporating auxiliary meta-data in NEXT. Meta-data

Acc@1

Acc@5

Acc@10

MAP

X

0.1007 0.1115

0.2173 0.2396

0.2793 0.3038

0.1615 0.1772

mendation accuracy in NEXT. Table 7 reports the performance with/without incorporating the associated friendship and textual description on CA. We observe that NEXT achieves significant better performance by incorporating auxiliary meta-data information. Note that α and β in Equations 11, 7 and 9 control the importance of the meta-data of POIs and users respectively. Here, these two parameters are tuned in the following way. First, we choose the optimal α value by fixing β = 1.0 (i.e., no meta-data is used for uesr-based intent calculation). Then the optimal β value is chosen by fixing this α value. Following this strategy, we set α = 0.3 and β = 0.2 for CA dataset. Figure 4 plots the performance of NEXT by varying β and α values after fixing α = 0.3 and β = 0.2 respectively. An obvious observation is that the performance of NEXT starts decrease as either α or β increases towards 1.0. The optimal range of β is [0.1, 0.3]. Also, the optimal range of α is [0.3, 0.6]. We argue that the meta-data information associated with the users could be more useful on CA dataset. Overall, the experimental results demonstrate that the proposed NEXT is competent to exploit the auxiliary meta-data for better recommendation accuracy.

5

Conclusions

In this paper, we propose a simple neural network framework for next POI recommendation, named NEXT. NEXT derives the spatial intent for a user by calculating POI-based intent and user-based intent separately based on two individual RELU nonlinearities. Under this framework, we can incorporate different contextual factors to enhance next POI recommendation in an unified architecture. Specifically, we incorporate two kinds of temporal context to enhance the intent calculation process. Furthermore, we adopt DeepWalk to encode the spatial constraints such as geographical information and sequential relations pattern into POI embeddings through a pre-training scheme. The experimental results over the three real-world datasets show that the proposed NEXT outperforms existing state-ofthe-art alternatives in terms of MAP and Acc@K. We further show that NEXT achieves better performance in the task of cold-start user recommendation and provide the semantic interpretability for the intent dimenions. This uniqueness makes NEXT an preferrable choice in real-world applications. As a future work, we plan to introduce the attention mechanism into NEXT for better recommendation accuracy.

Acknowledgment This research was supported by National Natural Science Foundation of China (No. 61502344, No.1636219, No.U1636101), Natural Scientific Research Program of Wuhan University (No. 2042017kf0225, No. 2042016kf0190), Academic

15

Team Building Plan for Young Scholars from Wuhan University (No. Whu2016012) and Singapore Ministry of Education Academic Research Fund Tier 2 (MOE2014-T2-2-066). Chenliang Li is the corresponding author.

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